Math Algorithms for Paintball (Recipes)

[tomcat]

Do you have an algorith (systematic method of solving a certain kind of repetitive problem) that could be useful to others in paintball?

[nerobro]

Paintball speed is not a constant. Time is a constant. the time between balls will remain the same as soon as you're INTO the string.

Given the balls are slowing down. 1/10 of a seccond later, the first ball will not have gone 30 feet.

As soon as you're sitting at say 60 feet you'll actually have 3 balls en route to you. and the balls will be physically closer togother. As the balls slow down they will come closer and closer to each other.

To create an accurate estimation of paintball distance we'd need to know how fast balls slow down. Balls are big, and have low mass, so they slow down really quickly.....

Actually calculating the gap gets pretty complex pretty quickly.

[nerobro]

it may work on constant velocity, but paintballs are never at a constant velocity.

I mention that the ball won't go 30 feet from the barrel in 1/10 of a seccond becuase that's the point that your guess would be closest to accurate. the further you go from the gun, the closer the balls get togother. ultimately they will start stacking on one another (but that would require shooting off a very tall cliff)

A more accurate algorythim would be based on time. But there's an unknown in the forumla we don't have on hand. That's the rate of acceleration of a paintball after it leaves the barrel.

IIRC the forumla for distance an object travels while accelerating is ViT+AT

now.. We know the initial veloicty, we know the time. And for any timeframe past the barrel of the gun we can easily calculate the distance between balls by taking one time value and adding .1 or whatever for the spacing between balls. Take the number from both timeframes and subtract the smaller number. and you have the distance balls are seperated at that range from the barrel.

so there's your algorythim. but you need to do the research to find out how fast a paintball will accelerate.

[Wat]

Nerobro is right. To find the gap between balls you'd find the time between balls * the ball speed where you want to know the gap. The gap between balls will be longer the closer you are to the shooter. The difference in gap length at 20 yards vs 30 yards is going to be substantial.

But the distance between shots is not that useful a number because the faster the ball, the distance is further but the balls clear it faster. If you're putting paint in a runners lane the time between shots is what counts.

However, nerobro your method isn't right. The formula ViT+AT is only useful in a frictionless or constant acceleration. The thing is we don't know how quickly the air resistance slows the ball.

[nerobro]

the rate of acceleration of the ball wont' be constant. You're right. becuase it's a Cd not a direct A... But the forumula was enough to make my point ;-) Drag is funny, it's calculated by the square of speed, and then it get's really screwed up when it stops. Stiction (static friction) has a whole other way of defining itself..

On a side note, most friction is a fairly steady number. it's that anoying fluid friction that really screws us up. and introduces innacuracy to our balls ;-)

[tomcat]

fps x 3600 / 5280

Sample:

280 x 3600 / 5280 = 190.90 miles per hour

[Wat]

Tomcat,

An easier thing to remember is that

60mph = 88fps

[314159]

30 mph = 44 fps !

.... just trying to help out ;)

[MasterYoda]

It is possible to find the acceleration of the ball after it exits the barrel. If one assumes that the flow is uniform and incompressible around the ball, then you can find the the drag force on the ball and use this to find the acceleration. Since the Reynolds number is on the order of 10^5 then you can assume that the skin friction is negligible since the aerodynamic drag will be much greater than any drag contributed due to friction. Cd for this case is approximately .4. An equation to approximate the aerodynamic drag is: Fd=1/2Cd*rho*V^2*A
Where rho is the density, which is assumed a constant for air at 1 atm and 20C. V is the velocity and A is the frontal area of the projectile. Sub this into Newton's 2nd law (sum(F)=m*(dV/dt)) and separarate the variables and integrate to get a function of change in velocity in terms of time. You can then use this equation to find a function of x in terms of t.

[whaarfrat]

This is a question from a non engineer, so be kind. I have thought that acceleration ceases when the ball goes beyond the effect of the propelling gas (i.e., just beyond the end of the barrel), and then begins deceleration as the air friction bleeds off its speed. You have been using the word "acceleration". It makes me very curious, and I'd appreciate it if you'd tell me how I have gone astray. Thanks, Peter "Wharf Rat" Simpson

[nerobro]

deceleration ins't a word ;-) Acceleration is a vector. and can occour in any direction. in the case of a paintball as soon as you reach the porting on the barrel the acceleration if negative.

[Redkey]

At 300 ft/sec how much pressure is the ball generating on it's leading edge? I have no idea... but, as long as the pressure in the barrel was higher than the resistance pressure, the ball would continue to accelerate. If the porting could not vent the air pressure fast enough then the ball will continue to accerate even after it has passed the porting. Only when the pressure behind the ball has dropped below the resistance pressure will the ball begin to decelerate... oh excuse me, have a negative acceleration vector.

So... saying that the ball stops accelerating once it passes the porting may not necessarily be true.

[MasterYoda]

Originally posted by Redkey

So... saying that the ball stops accelerating once it passes the porting may not necessarily be true.

True, but any acceleration during this time is negligible compaired to the acceleration beforehand and afterward because it occurs over such a short time span. It makes it easier just to leave it out and assume that the acceleration stops at the porting.

[Natural Newbie]

Well some barrels have more porting than others. So the decrease in acceleration could be critical in some and not in others. (I know it's an obvious statement, just trying to warm up to techie threads :D )

[NastyPTA]

so a paintball fired at 280f/s in a true vacuum over a 24 hr period will travel roughly 4581 miles?? damn, whole new meaning to long ball...better start working on my tactics

[nerobro]

Lets say teh ball is doing 200mph. the ball will have around a psi and a half on the front of the ball. the ball will begin to slow down as soon as the pressure behind the ball drops below the force needed to overcome that pressure, and the balls drag on the balls of the barrel.

For all intents and purposes, a ball will no longer gain velocity as soon as the ball enters the ported section of the barrel.

this is to say, that for a ball to shoot 300fps out of a barrel that has a lot of porting.. say 10" of porting (a reasonable number given a dye boomstick) the ball will need to be going signifigantly more than 300fps before the ball leaves the non ported section of barrel.

[Natural Newbie]

That sounds right.

Now correct me if I am wrong. If the ball is decelerating while its leaving the barrel vs. accelerating while leaving the barrel (lets say a 4 inch barrel with no ports) will the decelerating ball go less distance? Or will they both go the same since once they leave the tip of the barrel all deceleration is the same. (I know decelerating isn't technical but in racecar driver terms it is ;) )

[AGD]

So I think this thread brings up an interesting point. If you shoot at lower velocities and the balls are closer together, wouldn't it be harder to run through a paint stream????

I think that is worth looking into......

AGD

[SPB|ASH]

BlackVCG and I had an in-depth physics/differential equation conversation when we then decided that none of this actually mattered at all.

The Rate Of Fire is the only determining factor of the "difficulty" of running through a paint stream.

This is because paintballs are a set amount of TIME behind one another. Imagine shooting a lead ball at 300 fps. After 0.10 seconds (10 BPS), the lead ball is now traveling at 260 fps (made up number for demo purposes) and the 2nd ball comes out of the barrel at 300 fps. The 2nd ball will slowly "catch up" to the first ball distance wise over a period of time until both balls come to rest at the same spot.

If the balls leave the barrel at 500 fps, and 0.10 seconds later they are traveling at 400 fps (again a made up number for demo purposes) the same effect will be observed.

However, both balls will ALWAYS be seperated by a time of 0.10 seconds. If you look at a single "point" in space where the balls travel through, after 10 seconds, 10 balls will travel through that point, no matter the velocity.

This means that you need to run fast enough to clear that "point" without getting shot.

Now someone might also think that if you run fast enough, you can clear the space, but the fastest human runners (olympians) can run about 100m in 10 seconds. This roughly equates to about 33-35 fps, or 3.3 - 3.5 ft of maximum distance traveled between balls coming to the "point". (*Note: this means you have to enter the stream RIGHT as lead ball leaves and this gives you the MAX possible distance to travel before the next ball arrives and it also means you have to be an olympic sprinter in full paintball gear, but Ill roll with it anyways.).

I dont know about the rest of you, but when I am full on sprinting with my arms moving and my gun in my hands, im at least that long if not more. This means that I cannot run through a paint stream of 10 BPS ever, in theory [Im pretty sure BlackVCG isnt that fast either ;)].

Now if one does take into account ball spacings at certain intervals due to the width of your body and not just the length, you actually have even less time to clear the stream due to the fact that the "point" is now offset a little by the width of your body. And the closer the balls are, the harder it will be to run through the stream due to the offset.

I think that in conclusion to all of this, the "difficulty" of running through a paint stream is mainly dependent on the Rate of Fire with ball spacing being a secondary "added bonus" of NOT being physically capable of clearing the stream.

-SPB|Ash

PS, BlackVCG can shoot at 13 BPS (we have proof and video), and I know from personal experience that I CANNOT run through that ;).

[johnny dee]

ok. how many of u take physics , such as i do....all these guys are right, u can apply the mathematical formulas to the paintball aspect and get a round about answer to any problem, i say round about because every ball is different, you may not be able to visibly see it but they are.

[Redkey]

SPB|ASH

Aren't you making a large assumption that the balls actually fly staight? If you just happen to get one ball curving right while the next ball curved left... a window would be created in the stream.


johnny dee

While physics tell you what things should be doing... real testing is the only way to tell what they are doing. Lots of real testing will also enable you to statistically describe your system and predict it's performance.

nerobro

1.5 psi at 300 fps? Is that a real number or just an example?

[BlackVCG]

Redkey-

It is an assumption and you have to have a list of assumptions to consider the problem. Considering with a decent gun and decent paint the deviation of the paintball flight in the lateral direction is minimal, you might as well consider the balls to all fly on the same path.

Yes, there is the possibility of a window opening between two shots randomly throughout the paint stream, but it's such a moot point that it's really not worth considering when you're looking at a ROF around 10bps.

[nerobro]

Holdon, I have the actual book here right now. my post earlier was from home. at 200mph.. Wow I was way off. :-) .7psi A paintball is only... 0.36 sq in.... So the ball would see at be seeing .252lbs of force as soon as the ball left the barrel. That's the "real" number as to how much static pressure the front of the ball will see. But that number is constantly changing due to change in velocity. Aerodynamic pressure changes as a exponential function of speed... and THEN there's other forms of drag occouring, including induced drag from the turbulance it leaves behind itself, and surface drag from the texture of the ball...

[nerobro]

I think I"d like to chronograph paint at "range" like at 20-30-40-50-60 and 70 feet out.. so we can have some kind of idea what spacing we have between balls. when I DO run through a stream of paint, I"m usually dependant on a bouncer or two ;-) and when you're on the run, you tend to get that bounce you need. (I think that has to do with the way clothes fluff while running... )

Now back to AGD's idea.. In theroy if you're shooting crossfield and trying to create a wall of paint for other players to "try" to run through, your paint will be traveling relitively slowly anyway.

I do have a radar chrono... and I do have paint. I"ll do some testing this week. Hopefuly tonight. I think it's time I contributed to the mass of data that AGD has at his disposal.

[savitar]

MasterYoda has it down, but everyone forgot parasitic drag on smooth objects. Laminar flow. That's the reason golf balls have dimples. There called "trips" as they break up the laminar flow that causes turbulance, and negative pressure behind the ball. A new and improved paintball would track straight, and be more consistant would look like a golf ball, or a baseball (with stitches).

I must say you guys are way cool!:D